The Cramer-Rao Bound for channel estimation in block fading Amplify-and-Forward relaying networks

In this paper, we express the Cramer-Rao Bound (CRB) for channel coefficient and noise variance estimation at the destination of an Amplify-and- Forward (AF) based cooperative system, in terms of the a posteriori expectation of the codewords. An algorithm based on factor graphs can be applied in order to calculate this expectation. As the computation of the CRB is rather intensive, the modified CRB (MCRB), which is a looser bound, is derived in closed form. It can be shown that the MCRB coincides with the CRB in the high signal-to-noise ratio (SNR) limit and to that end the CRB/MCRB ratio is simulated in case of uncoded and convolutional encoded transmission.